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295. Find Median from Data Stream.cpp
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295. Find Median from Data Stream.cpp
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//Approach 1: Simple Sorting
//TLE
//15 / 18 test cases passed.
//time: O(NlogN), space: O(N)
class MedianFinder {
public:
vector<int> vec;
/** initialize your data structure here. */
MedianFinder() {
}
void addNum(int num) {
vec.push_back(num);
sort(vec.begin(), vec.end());
}
double findMedian() {
int n = vec.size();
if(n&1) return vec[n>>1];
return (vec[(n>>1)-1]+vec[n>>1])/2.0;
}
};
/**
* Your MedianFinder object will be instantiated and called as such:
* MedianFinder* obj = new MedianFinder();
* obj->addNum(num);
* double param_2 = obj->findMedian();
*/
//Approach 2: Insertion Sort
//Runtime: 444 ms, faster than 15.81% of C++ online submissions for Find Median from Data Stream.
//Memory Usage: 46.8 MB, less than 94.97% of C++ online submissions for Find Median from Data Stream.
//time: O(N+logN) = O(N), space: O(N)
class MedianFinder {
public:
vector<int> vec;
/** initialize your data structure here. */
MedianFinder() {
}
void addNum(int num) {
if(vec.empty()){
vec.push_back(num);
}else{
/*
lower_bound: find the smallest number >= x
if there is no such element, it returns vec.end(),
in this case, this statement is still safe
*/
vec.insert(lower_bound(vec.begin(), vec.end(), num), num);
}
}
double findMedian() {
int n = vec.size();
if(n&1) return vec[n>>1];
return (vec[(n>>1)-1]+vec[n>>1])/2.0;
}
};
//Approach 3: Two Heaps
//Runtime: 424 ms, faster than 18.81% of C++ online submissions for Find Median from Data Stream.
//Memory Usage: 47 MB, less than 41.77% of C++ online submissions for Find Median from Data Stream.
//time: O(logN), space: O(N)
class MedianFinder {
public:
//maxPQ: smaller half, may contain one more element than minPQ
//minPQ: larger half
priority_queue<int, vector<int>> maxPQ;
priority_queue<int, vector<int>, greater<int>> minPQ;
/** initialize your data structure here. */
MedianFinder() {
}
void addNum(int num) {
maxPQ.push(num);
int t = maxPQ.top(); maxPQ.pop();
minPQ.push(t);
//minPQ's size must be <= maxPQ's size
if(minPQ.size() > maxPQ.size()){
t = minPQ.top(); minPQ.pop();
maxPQ.push(t);
}
}
double findMedian() {
if(maxPQ.size() > minPQ.size()){
return maxPQ.top();
}
return (maxPQ.top()+minPQ.top())/2.0;
}
};
//Approach 4: Multiset and Two Pointers
//Runtime: 220 ms, faster than 95.39% of C++ online submissions for Find Median from Data Stream.
//Memory Usage: 49.3 MB, less than 9.29% of C++ online submissions for Find Median from Data Stream.
//time: O(logN), space: O(N)
class MedianFinder {
public:
//AVL tree
multiset<int> mset;
multiset<int>::iterator lo, hi;
/** initialize your data structure here. */
MedianFinder() {
}
void addNum(int num) {
int n = mset.size();
multiset<int>::iterator it = mset.insert(num);
if(!n){
//originally empty
lo = hi = it;
}else if(n&1){
//odd number of elements, lo and hi points to same location
if(num < *lo){
/*
[1,2,3]
becomes
[1,1,2,3]
*/
--lo;
}else if(num == *lo){
/*
In C++, if there are already elements equal to num,
then it insert num after such elements,
so larger half's size will increase
[1,2,3]: lo and hi points to 2
becomes
[1,2,2,3]: lo points to 1st 2, hi points to 2nd 2
*/
++hi;
}else{
//num > *lo
++hi;
}
}else{
//even number of elements
if(*lo <= num && num < *hi){
//note the <= and < here!!
/*
In C++, if there are already elements equal to num,
then it insert num after such elements
so when num equal to *lo,
it will also be inserted btw the two pointers
*/
lo = hi = it;
}else if(num < *lo){
/*
only when num < *lo(not ==),
num is inserted before lo
[1,3,4,5]
becomes
[1,2,3,4,5]
*/
hi = lo;
//lo and hi both points to old lo
}else{
/*
when num >= *hi,
num is always inserted after hi
[1,3,4,5]
becomes
[1,3,4,5,6]
*/
lo = hi;
//lo and hi both points to old hi
}
}
}
double findMedian() {
return (*lo + *hi)/2.0;
}
};
//Multiset and One Pointer
//Runtime: 300 ms, faster than 44.92% of C++ online submissions for Find Median from Data Stream.
//Memory Usage: 49.5 MB, less than 5.62% of C++ online submissions for Find Median from Data Stream.
class MedianFinder {
public:
multiset<int> mset;
//mid points to the lower median if mset have even elements
multiset<int>::iterator mid;
/** initialize your data structure here. */
MedianFinder() {
}
void addNum(int num) {
int n = mset.size();
mset.insert(num);
if(n == 0){
mid = mset.begin();
}else if(num < *mid){
/*
[1,3,4]
becomes
[1,2,3,4]
[1,3,4,5]
beocmes
[1,2,3,4,5]
*/
mid = (n&1) ? prev(mid) : mid;
}else{
//num >= *mid, num is inserted after mid
/*
[1,3,4]
becomes
[1,3,4,6]
[1,3,4,5]
beocmes
[1,3,4,5,6]
*/
mid = (n&1) ? mid : next(mid);
}
}
double findMedian() {
int n = mset.size();
return (n&1) ? *mid: (*mid + *(next(mid)))/2.0;
}
};